## Motley Fool Predicting Blowout Profit From iPad mini – But if you check their math

A blogger for Motley Fool is predicting  a blowout quarter for Apple. He writes,

You can put me in that group.

Millions of consumers agree. By my math, the Mini probably brought in \$2.2 billion in operating profit in fiscal Q1,

These are big claims. Note that he is predicting \$2.2 billion profit from just one product line and that too operating profit not gross margin. Just as a refresher, gross margin is revenue less Cost of Goods Sold (COGS) for that product line. Operating profit is after R&D, sales & marketing and other operational expenses.

In the last quarter Apple made \$11B in operating profit, so Motley Fool is predicting 20% increase over last quarter just due to iPad mini.

What is the basis for this? Well we know this blogger bought one and hence he believes millions did so as well. But after that we do not know how he did his math to show \$2.2B as operating profit.

Well I did some math as well, about three months ago, and published my math, model and assumptions. In my last article in GigaOm I wrote (these are numbers for full year, not just Q1),

At the low end they could possibly lose \$1.7 billion and at the high end they could make \$2.5 billion in profit. But the chances of both these scenarios are just 1 percent. And so realistically, considering all possible scenarios, the expected value of profit is half a billion dollars—and that is gross profit, not including marketing and other costs associated with iPad mini.

From my more rigorous statistical modeling I predicted the best case scenario is \$2.5 billion gross margin for the entire year and the chances of that happening are just 1%. So for Q1 numbers let us assume even distribution and divide my numbers by 4. That gives \$125 million as expected profit and \$625 million as 1% possibility.

How can Motley Fool predict such large numbers?

The first difference is I did statistical modeling that considered all possible scenarios and not just the best case scenario. If Motley Fool assumed,

“I bought it, so millions would buy”

Of course it would yield \$2.2B but that fails to say how likely is such a scenario. Only in statistical modeling we can not only state an outcome but also state how likely is that scenario. (You heard of Nate Silver?)

Second difference is I took into account the negative effect of iPad mini on other product lines. That is iPad mini is not all additive, there is cannibalization. Using customer research data I included that effect (accounting for the uncertainty in the cannibalization rate) in computing net profit from iPad mini.

Finally I am not sure if Motley Food did any math at all. They say Apple would sell 20 million total iPad units (mini and maxi?). Since last quarter Apple sold 15.4 million iPads last quarter that would mean 4.6 million iPad mini (and by their assumption there was no cannibalization). So \$2.2B in operating profit from mere 4.6 million units.

That is each unit contributed  \$478 in operating profit. Really? Far more than the likely ASP of iPad mini and more than gross profit from iPad line. What kind of investment analysis or math is that? I hear this site gives investment advice, I wonder.

Lastly, I do stand by my model. Just wait a week more and plug in the numbers from Apple’s earnings report into this model and find out.

Note: Some have pointed out in GigaOm comments section that I used too conservative a number for iPad per unit profit and that iSuppli had a different (higher) margin prediction. My mean was 32% with sigma of 4.6% while iSuppli says the numbers are 42%. Even if I adjusted my mean to use iSuppli numbers, my predicted BEST CASE (2% chance) gross profit will utmost go to \$0.8B per quarter and not  \$2.2B Motley Fool predicts.

## Now I Know My p(A), p(B), p(C) …

This is not a primer or a refresher on probability but let us start with some probability calculations anyway,

1. What is the probability of getting Heads when you toss a fair coin?
2. How about getting  8 when you roll a pair of fair dice?
3. I have a rod that is 1 meter long. I draw two random numbers between 0 and 1 and cut the rods into three parts using the random numbers as lengths of pieces. What is the probability the three pieces can be arranged as a triangle?

Some are easy, some are computationally intensive but eventually we can get to the answer. We arrive at the answer by counting – we count all possible outcomes (Sample Space N) and count the number of desired result ( n) and find the probability a n/N.  (I think the answer to 3 is 0.25)

This is the traditional (also known as frequentist approach (because it involves counting frequencies of events) to probability.

But consider these,

1. You see the techcrunch headline about a new startup. Just from that headline, what is the probability that the startup will be a big success?
2. You see a salon on Main St, what is the probability that the next customer who walks in will be named Jonathan?

These are not easy to answer – definitely not by counting the sample space or the outcomes. Probability in these cases ceases to be a ratio of two countable events and becomes a representation of hunch, degree of belief, gut feel or a hypothesis.

I said it, hunch, belief, gut feel …

Probability now becomes a measure of our certainty (or uncertainty) about the outcome.  We are in the realm of  Bayesian probability. Despite the esoteric name, we all practice this in our every day reasoning.

A hunch, belief or hypothesis  has to start somewhere.

In some cases we start with  a probability value that is no different from the traditional approach. We remember reading somewhere that 90% of startups do not go big. So we answer the startup question as, 10%.   Similarly, the answer to the freemium question is 3%.

In some cases, it occurs from our domain knowledge and years of experience working with a specific area.

In some cases, it just occurs to us and we “just feel it in our gut”. So we state that the probability of next customer being Jonathan as 17%.

A hunch, gut feel or belief is not all bad when that is all we can make.

But problems arise when we trust our guts or pay grades,  even in the presence of prior knowledge or fail to take new knowledge into account to improve our hunch.

1. We fail to recognize that our initial assessment of the probability is based on limited observations.  One cannot make claims about safety of nuclear reactors for the next 500 years based only on 60 years of observation.
2. We straddle unknowingly from probability being a degree of our belief to the traditional definition of ratio of observed events. If the belief /hunch itself is based only on limited knowledge and information then we stand to commit serious errors of decision making, confusing our belief with real likelihood of occurrence of events.
3. Since we tend to overstate our knowledge and suffer from optimism bias  we overestimate the probability of favorable events and underestimate the probability of less favorable events. We then confidently state our degree of belief as actual measure of likelihood of occurrence of an event.
4. We stick to our initial estimate even when we uncover new information. In the traditional approach to probability, the values do not change.
p(H) = p(T) = 0.5  for any fair coin
But in the Bayesian world, probabilities change when we learn new information.
For example, if you learn that the name of the salon is Rapunzel, you will restate the probability of next customer being Jonathan as a very low number.

Knowing p(A), p(B), p(C)  is not any more as simple as A, B, C.

Next time we state a probability value, let us stop and ask whether we are stating our belief or the real likelihood of an event.

Notes:

To the question of finding the probability of a free user upgrading to premium version, see here.

The answer to the triangle question is based on the sides rule for triangles.

For discussion of gut vs. mind see here.

For the need for evidence based marketing, see here.